New extensions of Popoviciu's inequality
Marcela V. Mihai, Flavia-Corina Mitroi-Symeonidis
TL;DR
This paper extends Popoviciu's inequality to h-convexity and convexity related to quasi-arithmetic means, broadening its applicability and including various applications.
Contribution
It introduces novel extensions of Popoviciu's inequality within h-convexity and quasi-arithmetic mean frameworks, expanding theoretical understanding.
Findings
Extended Popoviciu's inequality to h-convex functions
Generalized inequality to convexity with quasi-arithmetic means
Presented multiple applications of the extended inequalities
Abstract
Popoviciu's inequality is extended to the framework of h-convexity and also to convexity with respect to a pair of quasi-arithmetic means. Several applications are included.
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Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results · Optimization and Variational Analysis